通过使用辅助系统方法，我们给出了基于李雅普·诺夫稳定性理论的广义同步定理。最后，用数值例子来验证定理的有效性。

By using the auxiliary system method, a sufficient condition for GS is derived based on the Lyapunov stability theory. At last, numerical examples are presented which fit the theoretical analysis.

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介绍了黑洞理论和广义相对论中的几个重要疑难，涉及霍金辐射、信息佯谬、奇性定理和钟速同步，并给出了可能的解答。

Some major puzzles in black hole theory and General Relativity, including Hawking radiation, information puzzle, singularity theorem and synchronization of clock rate, are presented.

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